Answer:
[tex]a_{n}[/tex] = - 2 [tex](4)^{n-1}[/tex]
Step-by-step explanation:
There is a common ratio between consecutive terms , that is
r = - 8 ÷ - 2 = - 32 ÷ - 8 = - 128 ÷ - 32 = 4
This indicates the sequence is geometric with nth term
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Here a₁ = - 2 and r = 4 , then explicit formula is
[tex]a_{n}[/tex] = - 2 [tex](4)^{n-1}[/tex]
